116 SECTIONAL ADDRESSES 
the resistance of the structure, or is capable of elimination by comparison 
of the results of the theory with existing and successful structures of the 
same kind. In fact, he is often content, so to speak, with formule of 
interpolation, or formule which permit him to determine from known 
structures or given dimensions the proper proportions of other structures 
of different dimensions.’ 
In a masonry arch the line of thrust might occupy one of a variety of 
positions any of which would satisfy the requirements of equilibrium. 
For the purposes of design or estimating stability, some particular line 
must be chosen and this can only be done by making assumptions, the 
validity of which must have regard to the method of construction and the 
probable conditions of stress in the masonry. One of the assumptions 
referred to by Unwin relates to the position of the line of thrust at the 
crown or springings. Since Unwin wrote, one of the advances made 
has been the introduction of definite hinges, at the crown or at the spring- 
ing level, or at both places, to ensure the line of thrust passing through 
those points. These hinges render the problem of strength and stability 
much more definite, but with respect to arches without hinges the position 
is still very like that described by Unwin, although much has been done 
by comparing and analysing existing structures, and many ‘formule of in- 
terpolation’ have been proposed. In the monumental work by Séjourné,? 
particulars are given of all arches of appreciable size throughout the world: 
details of construction are given, and the proportions are analysed and 
compared. 3 
Up to the first half of the nineteenth century, knowledge of the strengths 
and characteristics of materials and of the branch of engineering science 
now known as ‘applied mechanics,’ was not sufficient to establish or 
disprove the accuracy of various theories relating to the design or stability 
of a masonry arch then in vogue or from time to time propounded ; 
efforts to make progress in the problem depended almost as much on 
dialectics as on mechanical principles. 
An interesting incident occurred at the time the bridge across the 
Thames at Blackfriars was proposed in 1759. Of the competing designs 
the one by the architect Mylne for a bridge with elliptical arches was 
chosen, although at that time only one bridge with elliptical arches 
existed—Ammanutis’ bridge in Florence. A design for a bridge with 
semi-circular arches was submitted by Gwyn, an equally well-known 
architect. Some persons objected to the elliptical arches, and even Dr. 
Johnson expressed himself on the stability of the two forms of arch. 
Boswell records that “ Johnson’s regard for his friend Mr. Gwyn induced 
him to engage in a controversy against Mr. Mylne, and after being at 
considerable pains to study the subject he wrote three several letters in 
the Gazetteer in opposition to his plan.’ Johnson’s letters appeared in 
the Gazetteer for December 1, 8, and 15, 1759, from which the following 
extracts are given :— 
“'Those who are acquainted with the mathematical principles of archi- 
tecture are not many; and yet fewer are they who will, upon any single 
2 Grandes Voutes, by Paul Séjourné, 1913-1916. 
